Re: Radiation's equivalence principle

ebunn@xxxxxxxxxxxxxxxxxxxxxx wrote:
In article <dscjn4$jed$2@xxxxxxxxx>,
Phillip Helbig---remove CLOTHES to reply <helbig@xxxxxxxxxxxxxxxxxxxxxxxx> wrote:
In article <SQSFf.10817$1n4.2693@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
"Lord Snooty" <bonzo@xxxxxxx> writes:
Why is that an accelerated charge radiates in a zero-valued
gravitational field, whereas a charge in free-fall in a non-zero
gravitational field does not? Doesn't this contradict Einstein's
Equivalence Principle? Are we in fact already assured, via measurement,
of the free-fall case's outcome?
For the definitive account, read http://arxiv.org/abs/gr-qc/9303025 .

2. I don't think that the author has justified his main conclusion,
which is that "purely local experiments" can distinguish a charge in
uniform acceleration from a charge at rest in a uniform gravitational
field.

I agree. Here's a simple gedanken that I think shows that no local
experiment can do so, given the equivalence principle:

Consider a small rocket with a bare charge suspended inside, and an
observer who can measure the EM field at rest with respect to the
rocket, anywhere within it; all other sources of the EM field are
negligible. With the rocket far from any massive objects and thrusting
with constant proper acceleration, at any given position within the
rocket the EM field will be constant in time[#], so this observer cannot
possibly _measure_ any radiation[@]. With the rocket at rest on a
(large) massive planet, the equivalence principle implies the same
result. So for both cases this observer must necessarily conclude there
is no radiation[@], and therefore no radiation reaction and no
observable difference between the two cases.

[#] Consider the instantaneously-comoving inertial frame
(ICIF) of the observer. In this frame the EM field is due
to the retarded position of the charge, so the charge is
slightly offset in position and has a small velocity relative
to the observer in this ICIF. At any time this relationship
remains the same (even though the ICIF is different) because
the _proper_ acceleration is constant. Since the observer
always measures the field in the then-current ICIF, the
observer measures the field to be constant in time (even
though it is not purely Coulomb).

[@] Note that ExB is nonzero, but the absence of any time
variation in either E or B implies no radiation. The
corresponding transport of energy and momentum is of
course constant in time and is offset by the mechanism
suspending the charge.

Note this depends on the rocket being small, and the acceleration being
uniform.

As I have remarked elsewhere, "radiation" can be a rather slippery
concept; but the time variation of the EM field (or lack thereof) is
definitive, and in this case gives a clear conclusion. I believe the
above reference's error is in not basing the conclusion on
_measurements_ made locally.

Tom Roberts tjroberts@xxxxxxxxxx

.

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